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EC1003
JANUARY EXAMINATIONS 2006
Subject
ECONOMICS
Title of Paper
EC1003 USING MATHS IN ECONOMICS
Time Allowed
One and One Half Hours (1½ Hours)
______________________________________________________________________________________________________
Instructions to candidates
THREE questions should be answered
The approved calculator (that is, Casio FX-83ES or FX-85ES) may be used
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1. The demand for a good is given by
qd =
3m 2
p
and supply is given by
qs = 5p - 11
where m is income and p is the price of the good.
(a)
If m = 2, what is the equilibrium price and quantity?
[30%]
(b)
Find the price elasticity of demand and income elasticity of demand.
[20%]
(c)
Find the elasticity of supply at the equilibrium you found in (a).
[10%]
(d)
Suppose that m = 2 and a per unit sales tax of
and quantity.
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is imposed. Find the new equilibrium price
[40%]
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EC1003
2.
The Demand for Printers and Print Cartridges is given by
Printers: qdx = 50 – 5px – 2py
Cartridges: qdy = 50 – 3py – 4px
The supply of Printers and Print Cartridges is given by
Printers: qsx = 5px - 6
Cartridges: qsy = 7py
where qsx and qsy are the quantities supplied of Printers and Cartridges, respectively; qdx and qdy are
the quantities demanded of Printers and Cartridges, respectively; and px is the price of Printers and py
is the price of Cartridges.
3.
(a)
Find equilibrium prices and quantities for both Printers and Print Cartridges.
[40%]
(b)
Find expressions for the own price elasticity of demand and cross price elasticity of demand
for Printers and calculate their values when the markets are in equilibrium. Are the goods
substitutes or complements?
[25%]
(c)
Suppose the government tells the sellers of Printers that they must set their price to be 1 unit
below the equilibrium value you found in (a). How will the quantities of the two goods that
will be demanded and supplied change as a result?
[35%]
Demand for a monopolist’s output is given by
P=8–Q
and his costs are given by the total cost function
TC = 10 + 15Q – 6Q2 + Q3
(a)
Find expressions for fixed costs (FC), average variable cost (AVC) and marginal cost (MC).
[20%]
(b)
Show that the MC curve intersects the AVC curve at its minimum point. Sketch the MC and
AVC curves on the same graph.
[30%]
(c)
Find an expression for the profit function.
[10%]
(d)
Given that the monopolist produces more than zero units, what output will it choose to
produce if it seeks to maximise its profits and at what price will it sell this output. What is
profit at this output? Would the monopolist be better off if he choose to produce zero units
instead?
[40%]
Continued …
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EC1003
4.
A firm operating in a perfectly competitive market has the short run average variable cost (AVC)
function
AVC = 1 – 3Q + 3Q2
and the fixed cost (FC) function
FC = 20
5.
(a)
Find an expression for the firm’s total costs (TC) and marginal costs (MC).
[20%]
(b)
Write an expression for the firm’s short run supply curve as a function of the market price, P.
[40%]
(c)
What is the lowest output the firm will supply. At what price will it supply this quantity?
What profit or loss does it make if it supplies this quantity? Briefly comment on your result.
[40%]
A consumer’s utility function is given by
U = 2x0.5y0.75
where x represents her consumption of good X and y represents her consumption of good y.
Her income is £100 and the price of good X is £15 while the price of good Y is £3.
(a)
Write down an expression for the indifference curve on which the point x = 9 and y = 16 lies.
[10%]
(b)
Suppose the consumer consumes 9 units of good X. How many units of good Y does the
consumer have to consumer to get onto the indifference curve you found in part (a). [10%]
(c)
What quantities of goods X and Y will the consumer consume in order to maximise her utility
subject to her budget constraint?
[50%]
(d)
Find expressions for the marginal utility of good X and the marginal utility of good Y.
Compute the ratio of the two marginal utilities at the values of x and y you found in part (c).
How does this compare to the ratio of the prices of the two goods.
[30%]
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6.
A firm has the following production function:
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EC1003
Q = 3L + 4K + 5LK
(a)
Explain whether this production function exhibits increasing, constant or decreasing returns to
scale.
[20%]
(b)
Write down expressions for the marginal product of labour and the marginal product of
capital.
Are there decreasing marginal returns to labour? Are there decreasing marginal returns to
capital?
[20%]
(c)
Suppose the firm can spend no more than £108 on both labour and capital, and buys labour at
£1 per worker and capital at £8 per unit. What is the firm’s maximum output?
[60%]
End of Paper
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